Various physics applications involve the computation of the standard hypergeometric function 2F1 and its derivatives. Because it is not an intrinsic in the common programming languages, automatic differentiation tools will either differentiate through the code that computes 2F1 if that code is available or require the user to provide hand-written derivative code. We present options for the derivative computation in the context of an ionization problems and compare the approach implemented in the Diamant library to standard methods.